Almost Sure Stability of Markov Jump Linear Systems With Deterministic Switching

Author

Bolzern, P. ; Colaneri, P. ; De Nicolao, G.

Author_Institution

Dipt. di Elettron. e Inf., Politec. di Milano, Milan, Italy

Volume

58

Issue

1

fYear

2013

fDate

Jan. 2013

Firstpage

209

Lastpage

214

Abstract

The technical note studies a class of linear systems whose piecewise-constant dynamic matrix is subject to both stochastic jumps, governed by a Markov chain, and deterministic switches. These systems will be dubbed switching dynamics Markov jump linear systems (SD-MJLS). Sufficient conditions for exponential almost sure stability (EAS-stability) are established under either hard or average constraints on the dwell-time between switching instants. The proof relies on easy-to-check norm contractivity conditions and the ergodic law of large numbers.

Keywords

Markov processes; asymptotic stability; dynamic programming; linear systems; matrix algebra; EAS-stability; Markov chain; Markov jump linear systems; SD-MJLS; deterministic switching; exponential almost sure stability; piecewise-constant dynamic matrix; stochastic jumps; switching dynamics Markov jump linear systems; Linear systems; Markov processes; Numerical stability; Stability criteria; Switches; Almost sure stability; Markov jump systems; dwell-time;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2012.2203049

Filename

6213076